orientations and misorientations, rotations taking coordinates in the frame CS to coordinates in the frame SS; a misorientation is one between two crystal frames

Syntax

ori = orientation(rot, cs, ss)

A rotation between a crystal and a specimen frame.

ori = orientation(a, b, c, d, cs, ss)

The quaternion coefficients.

mori = orientation(rot, cs, cs, antipodal=True)

A misorientation with grain exchange.

ori = orientation(f, points=100)

Points along a fibre.

ori = orientation.byEuler(phi1, Phi, phi2, cs, ss)

Euler angles, and the other constructors.

Description

An orientation is a rotation that carries the two frames it maps between: frameA, the crystal frame CS, from which it takes the coordinates, and frameB, the specimen frame SS or the second crystal frame of a misorientation, to which it takes them. The symmetries of both frames enter every comparison, angle, mean and plot. A frame left out is the triclinic crystal frame, or the default specimen frame. Coefficients are normalised; an improper transform is refused, an orientation is proper.

An orientation given keeps its frames unless others are named; a fibre is sampled at points orientations, an embedding projected back onto the orientations.

Input

`rot`	rotation, quaternion or orientation
`a, b, c, d`	the quaternion coefficients, numbers or arrays
`cs`	crystalFrame, the frame mapped from
`ss`	specimenFrame, or the second crystalFrame of a misorientation
`f`	fibre

Keywords

keyword	default	description
`antipodal`	`False`	a misorientation with grain exchange, between two frames of one crystal: the misorientation and its inverse are taken as one
`dtype`	`None`	the floating point type of the coefficients
`points`	`1000`	the number of orientations sampled along a fibre

Output

ori orientation

Properties

`frameA`	source frame of the mapping, usually the crystal frame
`frameB`	target frame, usually the specimen or a second crystal frame
`CS, SS`	aliases for frameA and frameB
`antipodal`	grain exchange symmetry for misorientations between the same crystal frame
`notIID`	whether the orientations come from spatially dependent map measurements
`data`	unit quaternion coefficients, with shape ori.shape + (4,)
`phi1, Phi, phi2`	Bunge Euler angles in radians

Used on

DefinitionAsCoordinateTransform, OrientationEmbeddings, FibreODFs, PoleFigure2ODFGhostCorrection, RotationFibre, SO3FunVectorValued

MATLAB’s orientation.orientation

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/orientation.orientation_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.

orientation.orientation